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Home/Chain Registry/Block #2,924,649

Block #2,924,649

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/15/2018, 11:34:41 PM Β· Difficulty 11.3568 Β· 3,920,199 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
a257663d2d4feb21658ddd310574be56486364bf820ea6a556a82092891f66aa
View on Chainz β†—

Difficulty

11.356806

Transactions

1

Size

201 B

Version

2

Bits

0b5b57a5

Nonce

357,264,528

Timestamp

11/15/2018, 11:34:41 PM

Confirmations

3,920,199

Merkle Root

40864ec4ef92dac3b71b85a88c6c070537da9f4974a1018dd613a21305f0e7e0
Transactions (1)
Coinbase40864ec4ef92da…13a21305f0e7e0
1 in β†’ 1 out7.7400 XPM110 B
AUhjokok…k5m93PZR
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.671 Γ— 10⁹⁡(96-digit number)
76718147857978749329…14459387229606901440
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
7.671 Γ— 10⁹⁡(96-digit number)
76718147857978749329…14459387229606901439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.534 Γ— 10⁹⁢(97-digit number)
15343629571595749865…28918774459213802879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.068 Γ— 10⁹⁢(97-digit number)
30687259143191499731…57837548918427605759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.137 Γ— 10⁹⁢(97-digit number)
61374518286382999463…15675097836855211519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁷(98-digit number)
12274903657276599892…31350195673710423039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.454 Γ— 10⁹⁷(98-digit number)
24549807314553199785…62700391347420846079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.909 Γ— 10⁹⁷(98-digit number)
49099614629106399570…25400782694841692159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.819 Γ— 10⁹⁷(98-digit number)
98199229258212799141…50801565389683384319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.963 Γ— 10⁹⁸(99-digit number)
19639845851642559828…01603130779366768639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.927 Γ— 10⁹⁸(99-digit number)
39279691703285119656…03206261558733537279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.855 Γ— 10⁹⁸(99-digit number)
78559383406570239313…06412523117467074559
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2924649

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock a257663d2d4feb21658ddd310574be56486364bf820ea6a556a82092891f66aa

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,924,649 on Chainz β†—
Circulating Supply:58,003,194 XPMΒ·at block #6,844,847 Β· updates every 60s
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